Sophomore. Currently reading the manual to this very big machine.

Some quotes:

"It is a deeper subject than I appreciated and, I begin to suspect, deeper than anyone yet appreciates. To see it whole is certainly a daunting, for the moment even impossible, task." (Robert Langlands, writing about the theory of automorphic forms.)

"Understanding what a theorem means is a prerequisite to understanding its proof." (Contemporary Abstract Algebra, pp. 82, Theorem 4.3.)

"Better known for other work." (Lara Pudwell, after referencing a result due to Ted Kaczynski.)

And from this Quora Q&A that was one day randomly recommended to me:

Q: As a professor, has there been a student you instantly recognized as a genius in the first week of knowing them?

A: Certainly. I have been doing part-time university teaching since 1977. Some symptoms of success:

1. Student is in class on time.
2. Student sits in front row if at all possible.
3. Student arrives to class prepared with textbook, notepad, pen or pencil, anything else required.
4. Student asks questions like “I don’t understand the third paragraph on page 34. Could you explain it please?” (Very likely there’s a slip of paper in student’s textbook at page 34.)
5. Student does not ask questions like “Do we have to know this for the test?”
6. Student comes to office hours and/or asks questions by email on the course website.
7. Student does not address me as “Professor Edwards”.

(Edward Williams)